Showing papers on "Denotational semantics published in 2005"

Minimal Recursion Semantics An Introduction

Abstract: Minimal recursion semantics (MRS) is a framework for computational semantics that is suitable for parsing and generation and that can be implemented in typed feature structure formalisms. We discuss why, in general, a semantic representation with minimal structure is desirable and illustrate how a descriptively adequate representation with a nonrecursive structure may be achieved. MRS enables a simple formulation of the grammatical constraints on lexical and phrasal semantics, including the principles of semantic composition. We have integrated MRS with a broad-coverage HPSG grammar.

Foundations of attack trees

Abstract: Attack trees have found their way to practice because they have proved to be an intuitive aid in threat analysis. Despite, or perhaps thanks to, their apparent simplicity, they have not yet been provided with an unambiguous semantics. We argue that such a formal interpretation is indispensable to precisely understand how attack trees can be manipulated during construction and analysis. We provide a denotational semantics, based on a mapping to attack suites, which abstracts from the internal structure of an attack tree, we study transformations between attack trees, and we study the attribution and projection of an attack tree.

Operational semantics of hybrid systems

Abstract: Hybrid systems are heterogeneous systems that include continuous-time (CT) subsystems interacting with discrete-event (DE) subsystems. They are effective models for physical systems interacting with software or experiencing discrete mode changes. This dissertation discusses an interpretation of hybrid systems as executable programs written in a programming language with a hybrid system semantics. The semantic properties of such a programming language affect our ability to understand, execute, and analyze a hybrid system model. This dissertation focuses on a few semantic issues that come in defining such a programming language, such as the interpretation of discontinuities in CT signals and simultaneous discrete events in DE signals, liveness property, and the consequences of numerical ODE solver techniques. The interactions between CT and DE subsystems and between DE subsystems themselves are captured by discontinuities in continuous-time signals and simultaneous discrete events in discrete-event signals. In order to precisely represent them in compute execution results, a two-dimension domain, called "super-dense time," is used as the domain for defining signals. This domain allows a signal to have multiple values at the same time point while keeping the values ordered. CT and DE subsystems are modeled as actors, which are functions that map a set of signals to another set of signals. In this way, a hybrid system model is just a network of actors interacting via signals. We can always transform a network of actors into a composite actor with feedback, where the function of the composition actor is the composition of functions of the component actors. The least fixed point solution to the function of the composite actor, which is a set of signals, gives the denotational semantics of the hybrid system model. The operational semantics takes the denotational semantics as a mathematical foundation and defines a set of rules for evaluating actors such that the least fixed point solution can be constructed. Rather than constructing the whole signals, the operational semantics only computes a discrete subset of the signals called a discrete representation of the signals. The constructive procedure is formalized with the Abstract State Machine semantics, where a hybrid system is treated as a state transition system and the rules specify how state transformations are performed. This operational semantics supports heterogeneous and hierarchical composition of different models of computation, such as CT, DE, finite state machines, and synchronous languages, and modular execution of the composition as a whole. This ability makes it easy to jointly model and design software controlled systems. The operational semantics proposed in this dissertation has been implemented in HyVisual, which is a software tool for modeling and simulating hybrid systems. HyVisual is part of the Ptolemy II software framework, which is available in open-source form at http://ptolemy.org.

Records and Record Types in Semantic Theory

Abstract: This paper explores possibilities for formulating linguistic semantics in terms of records and record types of the kind used in recent developments of Martin-Lof type theory. We will suggest that this gives us tools to develop a single theory which includes aspects of Montague semantics, Discourse Representation Theory, situation semantics and Head-Driven Phrase Structure Grammar. We will also argue that formulating these theories in terms of record types may provide us not only with a unified approach but also with certain improvements over the individual theories.

A Dialogue Game Protocol for Multi-Agent Argument over Proposals for Action

Abstract: We present the syntax and semantics for a multi-agent dialogue game protocol which permits argument over proposals for action. The protocol, called the Persuasive Argument for Multiple Agents (PARMA) Protocol, embodies an earlier theory by the authors of persuasion over action which enables participants to rationally propose, attack, and defend, an action or course of actions (or inaction). We present an outline of both an axiomatic and a denotational semantics, and discuss implementation of the protocol, in the context of both human and artificial agents.

Almost ASAP semantics: from timed models to timed implementations

Abstract: In this paper, we introduce a parametric semantics for timed controllers called the Almost ASAP (as soon as possible) semantics. This semantics is a relaxation of the usual ASAP semantics (also called the maximal progress semantics) which is a mathematical idealization that cannot be implemented by any physical device no matter how fast it is. On the contrary, any correct Almost ASAP controller can be implemented by a program on a hardware if this hardware is fast enough. We study the properties of this semantics and show how it can be analyzed using the tool HyTech.

Comparison of different semantics for time petri nets

Abstract: In this paper we study the model of Time Petri Nets (TPNs) where a time interval is associated with the firing of a transition, but we extend it by considering general intervals rather than closed ones. A key feature of timed models is the memory policy, i.e. which timing informations are kept when a transition is fired. The original model selects an intermediate semantics where the transitions disabled after consuming the tokens, as well as the firing transition, are reinitialised. However this semantics is not appropriate for some applications. So we consider here two alternative semantics: the atomic and the persistent atomic ones. First we present relevant patterns of discrete event systems which show the interest of these semantics. Then we compare the expressiveness of the three semantics w.r.t. weak timed bisimilarity, establishing inclusion results in the general case. Furthermore we show that some inclusions are strict with unrestricted intervals even when nets are bounded. Then we focus on bounded TPNs with upper-closed intervals and we prove that the semantics are equivalent. Finally taking into account both the practical and the theoretical issues, we conclude that persistent atomic semantics should be preferred.

A denotational semantics for stateflow

Abstract: We present a denotational semantics for Stateflow, the graphical Statecharts-like language of the Matlab/Simulink toolsuite. This semantics makes use of continuations to capture even the most complex constructions of the language, such as inter-level transitions, junctions, or backtracking. An immediate application of this semantics is a formal compilation scheme for the language.

Structuring structural operational semantics

Abstract: Defining a formal (i.e., mathematical) semantics for computer languages is the first step towards developing rigorous techniques for reasoning about computerprograms and specifications in such a language. Structural Operational Semantics (SOS), introduced by Plotkin in 1981, has become a popular technique for defining formal semantics. In this thesis, we first review the basic concepts of SOS and the existing meta-results. Subsequently, we enhance the state of the art in this field by offering the following contributions:• developing a syntactic format guaranteeing a language construct to be commutative;• extending the existing congruence and well-definedness meta-results to the setting with equational specifications;• defining a more liberal notion of operational conservativity, called orthogonality,and formulating meta-theorems for it;• prototyping a framework for checking the premises of congruence and conservativity meta-theorems and animating programs according to their SOS specification;• defining notions of bisimulation with data and formulating syntactic rule formats guaranteeing congruence for these notions;• proposing syntactic rule formats for guaranteeing congruence of strong bisimilarity and higher-order bisimilarity in the setting of higher order processes.

Verifying web services composition based on hierarchical colored petri nets

Abstract: Current Web services composition proposals, such as BPML, BPEL, WSCI, and OWL-S, provide notations for describing the control and data flows in Web service collaborations. However, such proposals remain at the descriptive level, without providing any kind of mechanisms or tool support for verifying the composition specified in the proposed notations. In this paper, we present to verify Web services composition by using CP-nets. CP-nets combine the strengths of Petri nets with the expressive power of high-level programming and have sound mathematical semantics. These services composition proposals can be transformed by transformation rules into CP-nets, which can be used to analyze the performance and to investigate behavioral properties such as deadlock or livelock by CP-nets tools.

Profunctors, open maps and bisimulation

Abstract: This paper studies fundamental connections between profunctors (that is, distributors, or bimodules), open maps and bisimulation. In particular, it proves that a colimit preserving functor between presheaf categories (corresponding to a profunctor) preserves open maps and open map bisimulation. Consequently, the composition of profunctors preserves open maps as 2-cells. A guiding idea is the view that profunctors, and colimit preserving functors, are linear maps in a model of classical linear logic. But profunctors, and colimit preserving functors, as linear maps, are too restrictive for many applications. This leads to a study of a range of pseudo-comonads and of how non-linear maps in their co-Kleisli bicategories preserve open maps and bisimulation. The pseudo-comonads considered are based on finite colimit completion, ‘lifting’, and indexed families. The paper includes an appendix summarising the key results on coends, left Kan extensions and the preservation of colimits. One motivation for this work is that it provides a mathematical framework for extending domain theory and denotational semantics of programming languages to the more intricate models, languages and equivalences found in concurrent computation, but the results are likely to have more general applicability because of the ubiquitous nature of profunctors.

Notions of bisimulation and congruence formats for SOS with data

Abstract: While studying the specification of the operational semantics of different programming languages and formalisms, one can observe the following three facts. First, Plotkin's style of Structural Operational Semantics has become a standard in defining operational semantics. Second, congruence with respect to some notion of bisimilarity is an interesting property for such languages and it is essential in reasoning. Third, there are numerous languages that contain an explicit data part in the state of the operational semantics. The first two facts have resulted in a line of research exploring syntactic formats of operational rules to derive the desired congruence property for free. However, the third point (in combination with the first two) is not sufficiently addressed and there is no standard congruence format for operational semantics with an explicit data state. In this article, we address this problem by studying the implications of the presence of a data state on the notion of bisimilarity. Furthermore, we propose a number of formats for congruence.

Semantics of declarative goals in agent programming

Abstract: This paper addresses the notion of declarative goals as used in agent programming. Declarative goals describe desirable states, and semantics of these goals in an agent programming context can be defined in various ways. This paper defines two semantics for goals, with one based on default logic. The semantics are partly motivated by an analysis of other proposals that have been done in the literature. Further, we establish relations between and properties of these semantics.

A formal semantics of timed activity diagrams and its PROMELA translation

Abstract: The lack of a precise semantics for UML activity diagrams makes the reasoning on models constructed using such diagrams infeasible. However, such diagrams are widely used in domains that require a certain degree of confidence. Due to economical interests, the business domain is one of these. To enhance confidence level of UML activity diagrams, this paper provides a formal definition of their syntax and semantics. The main interest of our approach is that we chose UML activity diagrams, which are recognized to be more tractable by engineers, and we extend them with timing constraints. We outline the translation of our semantics into the PROMELA input language of the SPIN model checker which can be used to check several properties.

A linear-logic semantics for constraint handling rules

Abstract: One of the attractive features of the Constraint Handling Rules (CHR) programming language is its declarative semantics where rules are read as formulae in first-order predicate logic. However, the more CHR is used as a general-purpose programming language, the more the limitations of that kind of declarative semantics in modelling change become apparent. We propose an alternative declarative semantics based on (intuitionistic) linear logic, establishing strong theorems on both soundness and completeness of the new declarative semantics w.r.t. operational semantics.

About declarative semantics of logic-based agent languages

Abstract: In this paper we cope with providing an approach to declarative semantics of logic-based agent-oriented languages, taking then as a case-study the language DALI which has been previously defined by the authors. This “evolutionary semantics” does not resort to a concept of state: rather, it models reception of events as program transformation steps, that produce a “program evolution” and a corresponding “semantic evolution”. Communication among agents and multi-agent systems is also taken into account. The aim is that of modeling agent's evolution according to either external (environmental) or internal changes in a logical way, thus allowing in principle the adoption of formal verification methods. We also intend to create a common ground for relating and comparing different approaches/languages.

Why timed sequence diagrams require three-event semantics

Abstract: STAIRS is an approach to the compositional development of sequence diagrams supporting the specification of mandatory as well as potential behavior. In order to express the necessary distinction between black-box and glass-box refinement, an extension of the semantic framework with three event messages is introduced. A concrete syntax is also proposed. The proposed extension is especially useful when describing time constraints. The resulting approach, referred to as Timed STAIRS, is formally underpinned by denotational trace semantics. A trace is a sequence of three kinds of events: events for transmission, reception and consumption. We argue that such traces give the necessary expressiveness to capture the standard UML interpretation of sequence diagrams as well as the black-box interpretation found in classical formal methods.

A uniform approach to logic programming semantics

Abstract: Part of the theory of logic programming and nonmonotonic reasoning concerns the study of fixed-point semantics for these paradigms. Several different semantics have been proposed during the last two decades, and some have been more successful and acknowledged than others. The rationales behind those various semantics have been manifold, depending on one's point of view, which may be that of a programmer or inspired by commonsense reasoning, and consequently the constructions which lead to these semantics are technically very diverse, and the exact relationships between them have not yet been fully understood. In this paper, we present a conceptually new method, based on level mappings, which allows to provide uniform characterizations of different semantics for logic programs. We will display our approach by giving new and uniform characterizations of some of the major semantics, more particular of the least model semantics for definite programs, of the Fitting semantics, and of the well-founded semantics. A novel characterization of the weakly perfect model semantics will also be provided.

Comparisons and computation of well-founded semantics for disjunctive logic programs

Abstract: Much work has been done on extending the well-founded semantics to general disjunctive logic programs and various approaches have been proposed. However, these semantics are different from each other and no consensus is reached about which semantics is the most intended. In this article, we look at disjunctive well-founded reasoning from different angles. We show that there is an intuitive form of the well-founded reasoning in disjunctive logic programming which can be characterized by slightly modifying some existing approaches to defining disjunctive well-founded semantics, including program transformations, argumentation, unfounded sets (and resolution-like procedure). By employing the techniques developed by Brass and Dix in their transformation-based approach, we also provide a bottom-up procedure for this semantics. The significance of our work is not only in clarifying the relationship among different approaches, but also shed some light on what is an intended well-founded semantics for disjunctive logic programs.

A game semantics of the asynchronous π-calculus

Abstract: This paper studies the denotational semantics of the typed asynchronous π-calculus. We describe a simple game semantics of this language, placing it within a rich hierarchy of games models for programming languages.A key element of our account is the identification of suitable categorical structures for describing the interpretation of types and terms at an abstract level. It is based on the notion of closed Freyd category, establishing a connection between our semantics, and that of the γ-calculus. This structure is also used to define a trace operator, with which name binding is interpreted. We then show that our categorical characterization is sufficient to prove a weak soundness result.Another theme of the paper is the correspondence between justified sequences, on which our model is based, and traces in a labelled transition system in which only bound names are passed. We show that the denotations of processes are equivalent, via this correspondence, to their sets of traces. These results are used to show that the games model is fully abstract with respect to may-equivalence.

On sampled semantics of timed systems

Abstract: Timed systems can be considered with two types of semantics – dense time semantics and discrete time semantics. The most typical examples of both of them are real semantics and sampled semantics (i.e., discrete semantics with a fixed time step e). We investigate the relations between real semantics and sampled semantics with respect to different behavioral equivalences. Also, we study decidability of reachability problem for stopwatch automata with sampled semantics. Finally, our main technical contribution is decidability of non-emptiness of a timed automaton ω-language in some sampled semantics (this problem was previously wrongly classified as undecidable). For the proof we employ a novel characterization of reachability relations between configurations of a timed automaton.

Context-free languages via coalgebraic trace semantics

Abstract: We show that, for functors with suitable mild restrictions, the initial algebra in the category of sets and functions gives rise to the final coalgebra in the (Kleisli) category of sets and relations The finality principle thus obtained leads to the finite trace semantics of non-deterministic systems, which extends the trace semantics for coalgebras previously introduced by the second author We demonstrate the use of our technical result by giving the first coalgebraic account on context-free grammars, where we obtain generated context-free languages via the finite trace semantics Additionally, the constructions of both finite and possibly infinite parse trees are shown to be monads Hence our extension of the application domain of coalgebras identifies several new mathematical constructions and structures

An overview of semantics for the validation of numerical programs

Abstract: In this article, we introduce a simple formal semantics for floating-point numbers with errors which is expressive enough to be formally compared to the other methods. Next, we define formal semantics for interval, stochastic, automatic differentiation and error series methods. This enables us to formally compare the properties calculated in each semantics to our reference, simple semantics. Most of these methods having been developed to verify numerical intensive codes, we also discuss their adequacy to the formal validation of softwares and to static analysis. Finally, this study is completed by experimental results.